Bivariate Hermite subdivision

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    Abstract

    A subdivision scheme for constructing smooth surfaces interpolating scattered data in $\mathbb{R}^3$ is proposed. It is also possible to impose derivative constraints in these points. In the case of functional data, i.e., data are given in a properly triangulated set of points $\{(x_i, y_i)\}_{i=1}^N$ from which none of the pairs $(x_i,y_i)$ and $(x_j,y_j)$ with $i\neq j$ coincide, it is proved that the resulting surface (function) is $C^1$. The method is based on the construction of a sequence of continuous splines of degree 3. Another subdivision method, based on constructing a sequence of splines of degree 5 which are once differentiable, yields a function which is $C^2$ if the data are not ‘'too irregular'’. Finally the approximation properties of the methods are investigated.
    Original languageUndefined
    Pages (from-to)847-875
    Number of pages29
    JournalComputer aided geometric design
    Volume14
    Issue number14
    DOIs
    Publication statusPublished - Dec 1997

    Keywords

    • Subdivision
    • EWI-16320
    • METIS-140424
    • IR-29790
    • Hermite interpolation
    • Bivariate splines

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